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THE SET OF RATIONAL NUMBERS

I. ADDITION WITHLIKE ” DENOMINATORS

DEFINITION OF ADDITION OF RATIONAL FRACTIONS
If a/b and c/b are rational numbers, then
 

 

   
1/5 + 2/5 =  

So,1/5 + 2/5 =
 

II. ADDITION WITH “ UNLIKE ” DENOMINATORS

But what if the fractions do not have the same denominator ?
For instance,1/3 + 1/4

But, how do we count this? We need to find a way to combine the two drawings to find the sum .
Let’s “build-up” each fraction:

Now, compare these two lists and look for a “like”
denominator. What is it? ________

AN INTERESTING PROPERTY
If a/b and c/d are any two rational numbers, then


 

EXAMPLES: Using the LCD Using the Above Property
   
   
   
   

III. MIXED NUMBERS
Mixed numbers are numbers that are the sum of an integer and a fractional part of an integer. For
example, if a nail is inches long, this means 2 inches plus an additional 3/4 inches. (It is
common to think that since 2y means 2 times y, that means 2 times3/4, but this is incorrect!)

Change the following mixed numbers to improper fractions.

Using the Coventional Algorithm Change with Meaning

Change the following improper fractions to mixed numbers.

Using the Coventional Algorithm Change with Meaning

IV.

PROPERTIES OF ADDITION FOR RATIONAL NUMBERS

Given any two rational numbers a/b and c/d where, b and d are non- zero integers :
1. Closure

2. Commutative

3. Associative

4. Additive Identity

5. Additive Inverse

For any rational number a/b there exists a unique
number ________ such that:

Name the additive inverse of the following:

V. ADDITION OF MIXED NUMBERS (Know how to add using the given mixed numbers)

VI. SUBTRACTION OF RATIONAL NUMBERS

SUBTRACTION OF RATIONAL NUMBERS

If a/b and c/d are any rational numbers, then

AN INTERESTING PROPERTY

If a/b and c/d are any two rational numbers, then

SUBTRACTION OF MIXED NUMBERS (Know how to subtract using the given mixed numbers

VII. ESTIMATION WITH RATIONAL NUMBERS

Many times when estimating with fractions, it is helpful to round to a convenient fraction –
for instance:0,1/2,1/3,1/4,1/5,2/3,3/4,or 1.

For example, if you got 59 out of 80 questions correct on your test, this is about 60/80 or 6/8 or 3/4

Then we can conclude that 3/4 is a HIGH ESTIMATE.

(You actually got less than 3/4 of the test correct, since 59 < 60, then 59/80< 60/80 = 3/4).

Approximate each of the following using 0,1/4,1/3,1/2,3/4,or 1.Tell if your estimate is low or high .

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